Removing a linear shift-invariant blur from a signal or image can be accomplished by inverse or Wiener filtering, or by an iterative least-squares deblurring procedure. Because of the ill-posed characteristics of the deconvolution problem, in the presence of noise, filtering methods often yield poor results. On the other hand, iterative methods often suffer from slow convergence at high spatial frequencies. This paper concerns solving deconvolution problems for atmospherically blurred images by the preconditioned conjugate gradient algorithm, where a new approximate inverse preconditioner is used to increase the rate of convergence. Theoretical results are established to show that fast convergence can be expected, and test results are reported for a ground-based astronomical imaging problem.

Cutaneous perfusion of the feet of normal volunteers and diabetic patients were measured by laser Doppler fluxmetry. A test paradigm was followed in which the feet were studied at room temperature, during cooling, and during rewarming after cooling. The data files were analyzed using sequential Fourier techniques on serial 20 second segments. Contour plots were generated from the resulting 120 Fourier spectra and compared between the diabetic patients and the normal volunteers. The use of contour plots was found to be helpful in differentiating the diabetic from normal foot plots during this type of stress testing. Significant portions of the power spectra were found in the low frequencies (0.1-0.2 Hz) but there was also a strong component corresponding to the cardiac cycle with at least one harmonic of that cycle observed at two times the heart rate. Diabetic patients exhibited reductions in cutaneous perfusion with cooling in both the low frequency and heart rate frequencies. Sequential spectral analyses arranged in contour plots provide significant information about cutaneous perfusion using laser Doppler fluxmetry and prove useful in evaluating other pathologies characterized by cutaneous perfusion abnormalities.>

A restructuring transformation that can be used to parallelize recurrence relations is described. The transformation is based on the hyperplane (or wavefront) method, but extends the applicability of the method to irregularly structured recurrences. It is assumed that the time of computation of an array element is a linear combination of its indices, and a variation of the simplex method is used to seek a succession of hyperplanes along which array elements can be computed concurrently. Portions of the work reported here have been implemented in the PS automatic program generation system.>